Norms allow system designers to specify the desired behaviour of a sociotechnical system. In this way, norms regulate what the social and technical agents in a sociotechnical system should (not) do. In this context, a vitally important question is the development of mechanisms for monitoring whether these agents comply with norms. Proposals on norm monitoring often assume that monitoring has no costs and/or that monitors have unlimited resources to observe the environment and the actions performed by agents. In this paper, we challenge this assumption and propose the first practical resource-bounded norm monitor. Our monitor is capable of selecting the resources to be deployed and use them to check norm compliance with incomplete information about the actions performed and the state of the world. We formally demonstrate the correctness and soundness of our norm monitor and study its complexity. We also demonstrate in randomised simulations and benchmark experiments that our monitor can select monitored resources effectively and efficiently, detecting more norm violations and fulfilments than other tractable optimization approaches and obtaining slightly worse results than intractable optimal approaches.